Monotone invariant clustering procedures

A major justification for the hierarchical clustering methods proposed by Johnson is based upon their invariance with respect to monotone increasing transformations of the original similarity measures. Several alternative procedures are presented in this paper that also share in the same property of invariance. One of these techniques constructs a hierarchy of partitions by sequentially minimizing a monotone invariant goodness-of-fit statistic; the other techniques construct a hierarchy of partitions by successively subdividing the complete set of objects until one partition class is defined for each individual member in the set. A numerical example comparing these alternative procedures with Johnson's two methods is duscussed in terms of a simplified computational scheme for obtaining the necessary hierarchies.     

Ultrametric hierarchical clustering algorithms

Johnson has shown that the single linkage and the complete linkage hierarchical clustering algorithms induce a metric on the data known as the ultrametric. Through the use of the Lance and Williams recurrence formula, Johnson's proof is extended to four other common clustering algorithms. It is also noted that two additional methods produce hierarchical structures which can violate the ultrametric inequality.     

On normal theory based inference for multilevel models with distributional violations

Data in social and behavioral sciences are often hierarchically organized though seldom normal, yet normal theory based inference procedures are routinely used for analyzing multilevel models. Based on this observation, simple adjustments to normal theory based results are proposed to minimize the consequences of violating normality assumptions. For characterizing the distribution of parameter estimates, sandwich-type covariance matrices are derived. Standard errors based on these covariance matrices remain consistent under distributional violations. Implications of various covariance estimators are also discussed. For evaluating the quality of a multilevel model, a rescaled statistic is given for both the hierarchical linear model and the hierarchical structural equation model. The rescaled statistic, improving the likelihood ratio statistic by estimating one extra parameter, approaches the same mean as its reference distribution. A simulation study with a 2-level factor model implies that the rescaled statistic is preferable.This research was supported by grants DA01070 and DA00017 from the National Institute on Drug Abuse and a University of North Texas faculty research grant. We would like to thank the Associate Editor and two reviewers for suggestions that helped to improve the paper.     

A Third Moment Adjusted Test Statistic for Small Sample Factor Analysis

Goodness-of-fit testing in factor analysis is based on the assumption that the test statistic is asymptotically chi-square, but this property may not hold in small samples even when the factors and errors are normally distributed in the population. Robust methods such as Browne's (1984) asymptotically distribution-free method and Satorra Bentler's (1988, 1994) mean scaling statistic were developed under the presumption of nonnormality in the factors and errors. This article finds new application to the case where factors and errors are normally distributed in the population but the skewness of the obtained test statistic is still high due to sampling error in the observed indicators. An extension of Satorra Bentler's statistic is proposed that not only scales the mean but also adjusts the degrees of freedom based on the skewness of the obtained test statistic in order to improve its robustness under small samples. A simple simulation study shows that this third moment adjusted statistic asymptotically performs on par with previously proposed methods and at a very small sample size offers superior Type I error rates under a properly specified model. Data from Mardia, Kent, and Bibby's (1980) study of students tested for their ability in 5 content areas that were either open or closed book were used to illustrate the real-world performance of this statistic.     

Mixture Model Tests Of Hierarchical Clustering Algorithms: The Problem Of Classifying Everybody

Due to the effects of outliers, mixture model tests that require all objects to be classified can severely underestimate the accuracy of hierarchical clustering algorithms. More valid and relevant comparisons between algorithms can be made by calculating accuracy at several levels in the hierarchical tree and considering accuracy as a function of the coverage of the classification. Using this procedure, several algorithms were compared on their ability to resolve ten multivariate normal mixtures. All of the algorithms were significantly more accurate than a random linkage algorithm, and accuracy was inversely related to coverage. Algorithms using correlation as the similarity measure were significantly more accurate than those using Euclidean distance (p < .001). A subset of high accuracy algorithms, including single, average, and centroid linkage using correlation, and Ward's minimum variance technique, was identified.     

Hierarchical clustering schemes

Techniques for partitioning objects into optimally homogeneous groups on the basis of empirical measures of similarity among those objects have received increasing attention in several different fields. This paper develops a useful correspondence between any hierarchical system of such clusters, and a particular type of distance measure. The correspondence gives rise to two methods of clustering that are computationally rapid and invariant under monotonic transformations of the data. In an explicitly defined sense, one method forms clusters that are optimally connected, while the other forms clusters that are optimally compact.I am indebted to R. N. Shepard and J. D. Carroll for many stimulating discussions about this work, and for aid in preparing this paper.     

对汉字字形识别层次模型的实验验证

该研究采用Ｊｏｈｎｓｔｏｎ和ＭｃＣｌｅｌｌａｎｄ的实验范式以合体汉字为实验材料对层次模型进行了实验检验。结果表明,以假字掩蔽模式代替特征掩蔽模式使字目标对部件目标的字优效应明显下降。这一结果支持了层次模型,即合体汉字的字形加工以部件识别加工为中介。但本实验还发现了真字掩蔽模式下的字优效应量比假字掩蔽模式下明显减少,这一结果表明,在字加工水平中存在着觉察器间的相互竞争。因此,合体汉字字形识别的部件中介模型有待进一步完善。     

Hierarchial chunking in sentence processing

In order to evaluate a left-to-right hierarchical chunking model of sentence perception, Johnson’s Hierarchical Clustering Scheme (HCS) technique was applied to data obtained from sentence intelligibility tests. One hundred and twenty Ss listened to sentences disturbed by white noise. After each presentation they wrote down what they had heard. For each sentence, a table of conditional probabilities p(j/i) was computed, where p(j/i) is the probability that word j had been correctly identified. given correct identification of word i. This was done for all i’s and j’s from the sentence. HCS analysis of the off-diagonal submatrices for which words i precede words j (“forward conditional probabilities ”) yielded satisfactory results. Apparently there is a latent hierarchical structure to these data. The large chunks that appear from these analyses do generally correspond to major syntactic constituents. Minor constituents, however, are very often not reflected in the chunking pattern.     

Geometric and semantic similarity in visual masking

Semantic and geometric or physical similarity were manipulated separately in a backward-masking situation. When the target was a word to be read aloud, formal similarity between the letters of target and mask facilitated target recognition, as did associative similarity. Masking a target word by its own anagram also facilitated whole word report. In contrast, formal similarity was inhibitory rather than facilitatory of report when the target was spelled letter-by-letter, rather than read whole. This was true even for the same target words whose whole report was facilitated by formal similarity. A model to account for this reversal in the broader context of the neural substrate of reading is advanced. It is proposed that letter and word processing are fundamentally different in that letters are recognized by hierarchical feature analysis while words are stored and recognized wholistically by diffuse and redundant networks. Implications of the results for the study of reading are discussed.     

Hierarchical organization as a determinant of sequential learning

Subjects learned a set of permutations of a base sequence of letters. A set of permutations either defined a hierarchical organization for the base sequence or did not. Sets that defined organizations led to more correct responses, and the pattern of interitem sequential dependencies revealed that subjects had learned the organization defined by a response set. Differences in learning could not be explained in terms of the frequency with which items occurred adjacently because that frequency was held constant for both organization-defining and organization-free response sets. The difficulty of learning a particular organization was related to the memory load induced by the organization, and those differences were more consistent with a model of sequential learning proposed by Johnson (1970) than they were with a model proposed by Estes (1972).     

An analysis of generative representation systems

Three ideas are basic to generative theory: (a) Subjects are assumed to attend to the relations among stimuli, extracting the transformations relating pairs of stimuli; (b) the set of abstracted transformations is decomposed or reduced to an elementary set of generators; (c) subjects use the elementary generators as the basis for judging similarity. The purpose of this paper is to illustrate these ideas with an experiment in which subjects were asked to rate the similarity between stimulus pairs. The stimulus materials consisted of the permutations of a 4-item pattern with the properties of a dihedral group which insured the existence of sets of elementary transformations. Three analytic techniques were used to determine the generator set of transformations abstracted by subjects. The first analysis consisted of a monotonic regression between dissimilarity ratings and the number of elementary generators of a given permutation. The residual variance of this monotone regression, suitably normalized, was used as a quantitative goodness-of-fit measure. For the stochastic analysis, cumulative distributions of dissimilarity ratings were obtained for permutations requiring one, two, or three generators. The idea was that permutations requiring fewer generators should be associated with distributions of lower dissimilarity values (higher similarity scores) as compared to permutations predicted to be transformationally more complex. The final analysis, a multidimensional scaling of dissimilarity ratings, converted subjects' ratings into spatial structures to determine whether individual subjects' ratings exhibited the predicted spatial arrangement. The monotone regression and stochastic analyses abstracted similar generator sets for individual subjects, some of which provided perfect fits to the data. Although the scaling analysis yielded similar estimates of generators, for some subjects, transformations with the same number of generators yielded unequal “cognitive” distances resulting in some-what deformed spatial structures for these subjects. It was concluded that the results generally supported a generative model as an approximation to subjects' representations of interstimulus relationships.     

Genetic and environmental influences on the Verbal-Perceptual-Image Rotation (VPR) model of the structure of mental abilities in the Minnesota study of twins reared apart

In previous papers [Johnson, W., & Bouchard Jr., T. J. (2005a). Constructive Replication of the Visual-Perceptual-Image Rotation (VPR) Model in Thurstone's (1941) Battery of 60 Tests of Mental Ability. Intelligence, 33, 417–430.] [Johnson, W., & Bouchard Jr., T. J. (2005b). The Structure of Human Intelligence: It's Verbal, perceptual, and image rotation (VPR), not Fluid and Crystallized. Intelligence, 33, 393–416.] we have proposed the Verbal, perceptual, and image rotation (VPR) model of the structure of mental abilities. The VPR model is hierarchical, with a g factor that contributes strongly to broad verbal, perceptual, and image rotation abilities, which in turn contribute to 8 more specialized abilities. The verbal and perceptual abilities, though separable, are highly correlated, as are the perceptual and mental rotation abilities. The verbal and mental rotation abilities are much less correlated. In this study we used the twin sample in the Minnesota Study of Twins Reared Apart to estimate the genetic and environmental influences and the correlations among them at each order of the VPR model. Genetic influences accounted for 67–79% of the variance throughout the model, with the exception of the second-stratum Content Memory factor, which showed 33% genetic influence. These influences could not be attributed to assessed similarity of rearing environment. Genetic correlations closely mirrored the phenotypic correlations. Together, these findings substantiate the theory that the entire structure of mental abilities is strongly influenced by genes.     

A multidimensional scaling analysis of 16 complex sounds

The INDSCAL multidimensional scaling model was used to investigate the distinctive features involved in the perception of 16 complex nonspeech sounds. The signals differed along four physical dimensions: fundamental frequency, waveform, formant frequency, and number of formants. Scaling results indicated that subjects’ similarity ratings could be accounted for by three psychological or perceptual dimensions. A statistically reliable correspondence was observed between these perceptual dimensions and the physical characteristics of fundamental frequency, waveform, and a combination of the two formant parameters. These results were further explored with Johnson’s (1967) hierarchical clustering analysis. Large differences in featural saliency occurred in the group data with fundamental accounting for more variability than the remaining dimensions. Further analysis of individual subject data revealed large individual differences in featural saliency. These differences were related to past musical experience of the subject and to earlier findings using similar signals. It was concluded that (1) the INDSCAL model provides a useful method for the analysis of auditory perception in the nonspeech mode, and (2) featural saliency in such sounds is likely to be determined by an unspecified attentional mechanism.     

Transformation and alignment in similarity

This paper contrasts two structural accounts of psychological similarity: structural alignment (SA) and Representational Distortion (RD). SA proposes that similarity is determined by how readily the structures of two objects can be brought into alignment; RD measures similarity by the complexity of the transformation that “distorts” one representation into the other. We assess RD by defining a simple coding scheme of psychological transformations for the experimental materials. In two experiments, this “concrete” version of RD provides compelling fits of the data and compares favourably with SA. Finally, stepping back from particular models, we argue that perceptual theory suggests that transformations and alignment processes should generally be viewed as complementary, in contrast to the current distinction in the literature.     

SEAT-DSR: Spatial and energy aware trusted dynamic distance source routing algorithm for secure data communications in wireless sensor networks

This paper propose a novel secure routing mechanism called Spatial and Energy Aware Trusted Dynamic Distance Source Routing (SEAT-DSR) algorithm for enhancing the network life time of wireless sensor networks. Here, the spatial information, energy level, and the effectiveness of data quality are equalized by the Quality of Service (QoS) based energy aware routing algorithms. In addition to this approach, a standard clustering algorithm is also incorporates for grouping the wireless sensor nodes based on the trust score, spatial information, energy level and the distance between the nodes. In this SEAT-DSR is also capable of making decision over the evaluation metrics that are decided and expressed the QoS. Moreover, a new hierarchical trust mechanism is also introduced in this model which adopts multi-attributes of many wireless sensor nodes according to the data communication speed, data size, energy consumption, and the recommendation. This new hierarchical trust method relies over an improved the sliding window time by considering the presence of various attacks frequency to identify the attackers by discovering their anomalous behaviour. The proposed SEAT-DSR is evaluated by conducting many experiments in a simulation environment that creates by using Network Simulator-2 (NS2). The experimental results of the proposed algorithm are proved that the average packet transfer rate is increased drastically than the existing secure routing methodologies.     

改进的认知诊断模型项目功能差异检验方法——基于观察信息矩阵的Wald统计量

Hou,de la Torre和Nandakumar(2014)提出可以使用Wald统计量检验DIF,但其结果的一类错误率存在过度膨胀的问题。本研究中提出了一个使用观察信息矩阵进行计算的改进后的Wald统计量。结果表明:(1)使用观察信息矩阵计算的这一改进后的Wald统计量在DIF检验中具有良好的一类错误控制率,尤其是在项目具有较高区分能力的时候,解决了以往研究中一类错误率过度膨胀的问题。(2)随着样本量的增加以及DIF量的增大,使用观察信息矩阵计算Wald统计量的统计检验力也在增加。     

Degrees of algorithmic equivalence between the brain and its DNN models

Deep neural networks (DNNs) have become powerful and increasingly ubiquitous tools to model human cognition, and often produce similar behaviors. For example, with their hierarchical, brain-inspired organization of computations, DNNs apparently categorize real-world images in the same way as humans do. Does this imply that their categorization algorithms are also similar? We have framed the question with three embedded degrees that progressively constrain algorithmic similarity evaluations: equivalence of (i) behavioral/brain responses, which is current practice, (ii) the stimulus features that are processed to produce these outcomes, which is more constraining, and (iii) the algorithms that process these shared features, the ultimate goal. To improve DNNs as models of cognition, we develop for each degree an increasingly constrained benchmark that specifies the epistemological conditions for the considered equivalence.     

粗糙集和神经网络在心理测量中的应用

探讨当因素分析和多元回归方法的使用条件未得到满足时,是否可采用粗糙集方法进行观察变量的精简,以及是否可采用神经网络方法进行预测效度检验。理论分析了粗糙集和神经网络在心理测量中应用的可能性,并运用粗糙集对于人事干部胜任力评估数据进行分析,比较了7种离散化方法和2种约简算法构成的14种组合,发现当采用Manual方法进行离散化、遗传算法进行约简时,能够很好地对观测变量进行精简;运用概率神经网络能够比等级回归方法更好地进行预测效度检验。研究结果表明对于处理心理测量中的非等距变量,粗糙集和神经网络是非常有用的方法     

A theory of appropriate statistics

A formal theory of appropriateness for statistical operations is presented which incorporates features of Stevens' theory of appropriate statistics and Suppes' theory of empirical meaningfulness. It is proposed that a statistic be regarded as appropriate relative to statements made about it in case the truths of these statements are invariant under permissible transformations of the measurement scale. It is argued that the use of inappropriate statistics leads to the formulation of statements which are either semantically meaning-less or empirically nonsignificant.This research was supported in part by each of the following grants: National Science Foundation Grant GS-333 to the University of Oregon; National Science Foundation Grant to the Institute of Human Learning, University of California, Berkeley; and National Institute of Mental Health Grant MH-08055-01 (under the direction of Ernest W. Adams), also to the Institute of Human Learning. Work on this project was carried out in part during Robert F. Fagot's tenure as Public Health Service Special Fellow (No. MSP-15800) at the University of California, Berkeley, 1962-63; and during Richard E. Robinson's tenure as National Science Foundation Science Faculty Fellow at Stanford University, 1962–63.